In this paper we study the adaptive prefix coding problem in cases where
the
size of the input alphabet is large. We present an online prefix coding algorithm that uses
O(σ1 / λ + ε) bits of space for any constants
ε>0,
λ>1, and
encodes the string of symbols in O( log log σ) time
per symbol
in the worst case, where σ is the size of the alphabet.
The upper bound on the encoding length is
λ n H (s) +(λ ln 2 + 2 + ε) n +
O (σ1 / λ log 2 σ)
bits.